Electric-field distributions in two-dimensional arrays of gold nanodisks on Si3N4 membranes are modeled, using the discrete-dipole approximation, as a function of nanodisk diameter (20 − 50 nm), height (10 − 100 nm), ratio of the array spacing to diameter (1.3−4.7), and angle of incident light. The primary focus is on fields in a plane near the circular gold/vacuum interface with light of 532 nm wavelength incident through the membrane, a configuration that is particularly relevant to potential applications in plasmon-mediated Brillouin light scattering, photolithography, and photovoltaics. The average intensity over this plane increases with decreasing array spacing and incident angle relative to the substrate normal, partly because of increased excitation of a quadrupolar surface-plasmon mode. The height/diameter ratio for maximum intensities is between 0.7 and 1.5 and not strongly dependent on the spacing for a given angle.